SOL~ICATlOr~ PROCESSING TN 630 ,f-53 McGRAW-HILL SERIES IN MATERIALS SCIENCE AND ENGINEERING Editorial Board MICHAEL B. BEVER M. E. SHANK CHARLES A. WERT ROBERT F. MEHL, Honorary Senior Advisory Editor AVITZUR: Metal Forming: Processes and Analysis AZAROFF: Introduction to Solids BARRETTANDMASSALSKI:Structure of Metals BLATT:Physics of Electronic Conduction in Solids BRICK, GORDON,ANDPHILLIPS: Structure and Properties of Alloys BUERGER:Contemporary Crystallography BUERGER:Introduction to Crystal Geometry DE HOFFANDRHINES: Quantitative Microscopy DRAUGLIS,GRETZ, ANDJAFFEE:Molecular Processes on Solid Surfaces ELLIOTT: Constitution of Binary Alloys, First Supplement FLEMINGS:Solidification Processing GILMAN:Micromechanics of Flow in Solids GORDON: Principles of Phase Diagrams in Materials Systems GUY: Introduction to Materials Science HIRTH ANDLOTHE:Theory of Dislocations KANNINEN,ADLER,ROSENFIELD,ANDJAFFEE:Inelastic Behavior of Solids MILLS,ASCHER,ANDJAFFEE:Critical Phenomena in Alloys, Magnets, and Super-conductors MURR: Electron Optical Applications in Materials Science PAULANDWARSCHAUER:Solids under Pressure ROSENFIELD,HAHN, BEMENT,ANDJAFFEE:Dislocation Dynamics ROSENQVIST:Principles of Extractive Metallurgy RUDMAN,STRINGER,ANDJAFFEE:Phase Stability in Metals and Alloys SHEWMON:Diffusion in Solids SHEWMON:Transformations in Metals SHUNK: Constitution of Binary Alloys, Second Supplement WERTANDTHOMSON:Physics of Solids McGRAW-HILL BOOK COMPANY New York St. Louis San Francisco Dusseldorf Johannesburg Kuala Lumpur London Mexico Montreal New Delhi Panama Rio de Janeiro Singapore Sydney Toronto MERTON C. FLEMINGS Abex Professor of Metallurgy Massachusetts Institute of Technology Solidification Processing This book was set in Times Roman. The editors were B. J. Clark and Michael Gardner; the production supervisor was Joan M. Oppenheimer. The drawings were done by John Cordes, J &R Technical Services, Inc. The printer and binder was The Maple Press Company. Library of Congress Cataloging in Publication Data Flemings, Merton C 1929- Solidification processing. (McGraw-Hill series in materials science and engineering) Includes bibliographical references. 1. Solidification. 2. Alloys. I. Title. TN690.F59 669'.9 73-4261 ISBN 0-07-021283-x SOLIDIFICA nON PROCESSING Copyright © 1974by McGraw-HilI, Inc. All rights reserved. Printed in the United States ofAmerica. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise,. without the prior written permission of the publisher. 567 89-MAMM-76 54321 CONTENTS .. ~~T~:J.>fJ~~:\"",1- ~- r.. ,. '''' " , ~OT clVr·.:...·H···.:~J~~1(!:J.;J;H.;J.~)fl~.r Preface IX 1 Heat Flow in Solidification Growth of Single Crystals 1 Solidification of Castings and Ingots' 5 Casting Processes Employing Insulating Molds 6 Casting Processes in which Interface Resistance is Dominant 12 r;(Analytic Solutions for Ingot Casting 17 Solidification of Alloys 21 Problems in Multidimensional Heat Flow 24 2 Plane Front Solidification of Single-phase Alloys 31 Introduction 31 Equilibrium Solidification 33 No Solid Diffusion 34 Limited Liquid Diffusion, No Convection 36 Effect of Convection 41 Czochralski Growth (Crystal Pulling) 44 vi CCOSPNoleaTllEnilNdueTilfSairFcarotSinootnlidSifooiflciadCtiifaoisnctaintigosn aonfdPIonlgyopthsase Alloys 111111111111111111199456773345455677888956011122360014553417727446493863535738444570750572611 435 TGICCFCDCSTCSILRnnIPCTFNOCMEEGFTSDShoooearoeereointtyefoaeraoerlteqmllferlolrnotdretfiriumlnllfrychoscrwreamludlcsuununetinfettFaeueserdiSSturid-eaalsdcasEctnflipatrtatromaasuhrittpllttiatceateyrrxueoterairufcbuscRiledacdyaonuT-iorStaeetrGelntartcceote-eaoniADeacifedgdtwtteNoaiocSrtfADirgEdrtyrniuotleouCnutSnAEonetrioilouDGgiSlernoawnsraoocagct-SlonfeftrentaibdfStpoltpnyirfearmnnttfhufbdaeirhyhrhUtiGscatDfAvgleirabauiicirSoasiituctenolielntrntciuticenisSfeteewusycocsSnctdedtnteitayppuiwtUoeoseCidFoliGGTaterTdyornilSFhrtnneercrnichharisnrrydtrcasditoooaineranVesotsCeuwoniwoductsgonroaclsrotErfctetliyliteolhPhlioostuuCdaunsrirnotrtomgeeieoelSlnMolfecsfelnSetafdtuaairHenoClcrDbrladleitMiiorgsidlGdSrnihCeteSrtsyGclroetoPtuitlswlrtileciuoodrttFenwhufineoafrticetlrhcslmtsyaiotDaintSoiinrooenlcidtiiofinesd Eutectics Zone Melting FNTSlohuuleciirddlmeiafoiFtcidloaoyntwnioanmanicdosfIPntooelfryfpSahcoealisdeiKficiAnaetliltooicnyss: Castings and Ingots CONT2222222222222222222222222222211111111E5779889012233446667790001167N178899788259046089494946334345T0374572477813703S vii 789 PECEMPSSEDGFIGFCQPTRIRMIBAHEBTMCHnnnereuouaolufhfhoiiiiiaauoneoioturttfcaotssnlstfnsmrrreerestnitaemeiuenmeioceetsmeoivtoeaasrdnvcccnetcoorrrandrrordPedERpeIoittoiittaectgoytrylMdtrmienntiuiuaoevgyqtctseycroctogoanRiiggcrccaseoteeumAAoaecfnetfridtitttgdpneiISSiotynintniiisAPtllrloPenoiroCdcvyeSinlltooiieoeruvooocbGrntnoielIooullingiselolrenyynoiirauScooiuulrtaeddsaifdnlssicfrvsAuoyfssssstdiii;;aliaffuRiGbmlsLMFuitsotLboiiiNtfhruMSNccdpsaluinaynieituqaeiaatcietutqsrhusoiSfiateiuttaecocBoueeidiicnBbthtictPoolnrailidssuelaadiueonnLoseFaabpt-atlnr-oiiPltliaSkbeotpioqsionfinblosloshnuowueLlMinlTainestCoidiysd-Feqfa-epaSroauScsPhnooSnrritoEaahnmdoludlisrqIasidryeardSseufGotaegioinlAcsoIrErlisnaeeinblqdigtlrneuEoiiafruiytniflimRcsiaeobacrenrtgefiiioyunnmement 6 viii CTTPOaaNrbbTolEuecNlseTaSstoisoifnnAgpopfarnEodxrriomPrraotFepuenTrcthtiieeosrnmsal Data 333333333333333333330033344001112455245589158191528984698767 B ACLGGGMPGSFMEroeafolrrrraoefirtoooolngeelrcupwwwwlticnrhteeitaitniettttaarosclhhhhtdunbni,oeoilGcebbbfMCsPuTaryyyseWoloIrooamrewTPSrforPoGaplrcwptntrriCohhrmrtkooooiepooispcew-wnalli,edonutggterigtmaDahtmsiinteeiinedsossanlnorsMociofaSoanttEfriratouqeTlncunwstNisuaiitnruxiececsPldelIaarCtnoiaeonssnst Structures A Homogenization 10 IAnpdpeexndixes Growth PREFACE This book has grown largely out ofalecture course givento senior-leveland graduate students at Massachusetts Institute of Technology. It is intended for use in courses of this type, and also for the practicing engineer and research worker. The essential aim ofthe book isto treat the fundamentals of solidification processing and to relate these fundamentals to practice. Processes considered include crystal growing, shape casting, ingot casting, growth of composites, and splat-cooling. The book builds on the fundamentals of heat flow, mass transport, and inter face kinetics. Starting from these fundamentals, the basic similarities of the widely different solidification processes become evident. Problems at the end ofeach chapter relate principles to practice, illustrating important differences, as well as similarities between processes. Two years of college-level mathematics provides ample back ground for solving the problems given and for adequate comprehension of the text. In addition, it is desirable, though not necessary, that the student have a previous course in structure ofmaterials. Emphasis ofthe book ison metallic alloys, but other materials are also considered. An essential element of all solidification processes is heat flow. This subject is treated in the first chapter, primarily to lend cohesiveness to the material to follow. Itprovides anexcellentbasisfordescription and comparison ofsolidification processes, and itcanbetreated with rather simpleassumptions regarding the solidification mech anism. Chapter 2deals with mass transport ("solute redistribution") in single-crystal growth. A quantitative description oftransport in this type of solidification is"greatly simplified by the fact that the liquid-solid interface is single phase and planar. Equations derived in this chapter are also useful in describing dendritic solidification, except that they must be applied to tiny regions on the order of the dendrite arm spacmg. Chapter 3deals with the important question of how to maintain a plane front incrystal growth, and ofhow solute redistribution occurs when the plane front breaks down to form "cells." Plane-front solidification isconsidered again in Chap. 4, this time for polyphase alloys, such as eutectics and off-eutectic "composites" solidified with an essentially planar liquid-solid interface. This chapter isthe first to utilize the